Rigid Bodies copied from one file to another don't work
There are a couple of topics in this question actually, so I'm going to cover them separately.

Copying Rigid Bodies objects between files

As you did, copying is simple as Ctrl C and Ctrl V.

In my case (running 2.77 RC1) when you paste the objects they keep the highlighted green. 

What this green means is that the object is assigned to a Group. When working with Rigid Bodies, Blender add them to a group named RigidBodyWorld automatically. This is the way Blender knows what objects are into the simulation.

If you don't have your objects in the group, add them manually.

In case that you don't have Rigid Bodies working simulations into your scene:


Select all the objects you pasted
Press Ctrl G
Go to the operator panel (at the bottom of the Tool Shelf) or press F6 and change the name to RigidBodyWorld.


If you have other working Rigid Bodies into your scene, add them to the existing RigidBodyWorld group:


Select all the objects you pasted
Also select one of the existing Rigid Bodies in your scene, having this last object as the Active Object.
Press Shift Ctrl G
Select RigidBodyWorld on the pop-up menu.


Making your Rigid Body World work

Now, you have all the objects into the RigidBodyWorld group and they have all they Rigid Body properties as they had in the file where you copied them. But, if you are into a scene with no simulations, they'll don't work.

When you add a Rigid Body, Blender creates a Rigid Body World automatically, but if you are copy/pasting objects between scenes, you have to active the Rigid Body World manually.


Into the Properties window, go to the Scene tab and look for the Rigid Body World panel. Activate it.





Click the Group Field and select RigidBodyWorld


Now, if you play animation, you'll see that your Rigids Bodies are working just like in their original file.

Simulation VS Animation

Just a clarification: when you paste Rigid Bodies, you are not copying their animation because there's no animation linked to them. 

Animation stores within an object as keyframes, and simulation does by caching. The simulation cache is a group of files that stores the transformation of the objects in every frame. Contrary, the keyframes just store this information in some frames and Blender interpolates the movement between them.

So there's no way to copy the simulation itself into a new file by pasting the Rigid Body objects until you convert the simulation into keyframes by Baking the simulation. Here there's a question which covers that: Baking rigid body transformations